His coach was all business before the round. His caddie was in tears afterward. Only Phil Mickelson seemed to know how many magical moments he was capable of unfurling in between.

“I said, “Even-par or 1 under could win this thing.’ He said, ‘I’m going to be better than that,’” coach Butch Harmon recalled.

Harmon was standing near the 18th green in the fast-fading light of a cool Scottish summer afternoon. The roars from one of the great closing rounds in major championship golf was still ringing in his ears. He paused long enough to crack a wide smile.

“He wasn’t lying.”

Little more than 10 yards away, just after exiting the front door of the Muirfield clubhouse, caddie Jim “Bones” Mackay was still trying to regain his composure.

Someone asked about the tears he kept choking back. Instead, they started falling again.

“Because,” Mackay began, then turned away for nearly a half-minute. “When you work with someone for so many years, it’s pretty cool when you see him play the best round of golf he’s ever played in the last round of the British Open.”

This was the one major championship Mickelson never thought he could win. He came out on tour in 1992 oozing talent, a prodigy who won his first pro tournament while still in college, only to become another golfer once labeled the “next Nicklaus” who couldn’t break through in a major. Mickelson was 0-for-42 in that department and a dozen years into an otherwise stellar career when he finally won the Masters in 2004.

Another major came the next year at the PGA Championship. Then two more at the Masters. Along the way, he collected a record six runner-up finishes at the U.S. Open, the last just a month ago at Merion Golf Club, when Englishman Justin Rose zoomed by him on the final few holes.

Those were heartbreaks, to be sure, but at least Mickelson knew he had a shot on any golf course where booming drives and sky-high lob shots could decide the outcome. Despite playing on this side of the Atlantic for 20 years, though, he struggled trying to keep the ball under the wind and his temperament in check whenever he got a crazy bounce — and there were dozens of those.

For the longest time, links golf appeared to be one puzzle he was never going to unlock.

“It’s been the last eight or nine years I’ve started to playing it more effectively, I’ve started to hit the shots more effectively,” Mickelson said. “But even then it’s so different than what I grew up playing. I always wondered if I would develop the skills needed to win this championship.

“And to finally capture this,” he added a moment later, referring to the claret jug he was holding, “it feels really, really good.”

Just last week, 3 1/2 hours drive up the coast from here, he won the Scottish Open, his first-ever win on the continent. But Castle Stuart wasn’t a true links, and even an opening-round 69 across the fast, firm ground here failed to erase nearly two decades of doubt — especially when Mickelson complained about the condition of the course afterward.

But Mackay saw things differently.

“When he got to 18 on Thursday, he hit the best shot he hit all day and then three-putted. I think that kind of reinforces that stuff happens over here that you really can’t control,” Mackay said. “That you’re going to hit good shots and it’s not going to work out, and you suck it up and you move on.

“And the tournament could have gotten away from him, too, in the fairway bunker on 15 yesterday. And he didn’t let it, you know what I mean? Suck it up and move on. That’s what he did. He was just in a great place all week.”

Yet if Mickelson was going to crack, the place and time to do it Sunday would have been at the par-3 16th. He’d already clawed his way back from a 5-shot deficit and into the lead. His iron off the tee pierced the wind with a low trajectory and scooted onto the green at just the right speed to hold. Instead, it skittered off the right side and into a bunker.

“That was a bad break, but I was probably more bothered by it than he was,” Mackay said. “We walked up there. He saw it and said, ‘I can get it up and down.’ Pretty matter of fact. So I went, ‘Cool.’”

Mickelson did, then birdied No. 17, and walked up with a chance to do same at the 18th. A crowd of thousands packing the grandstands on either side of the fairway rose to their feet as one, clapping wildly. Mickelson made that curling left-to-right 10-footer to slam the door on the field behind him. Somehow, at 43, Mickelson isn’t simply holding his own, he appears to be turning back the clock.

“He’s stronger than he’s ever been. He’s fitter than he’s ever been. He’s hungrier than he’s ever been and you can understate how much he wants to compete and do well,” Mackay said.

“I joke around with him all the time that when he’s 60 on the putting green at Augusta, he’s going to say, ‘I got a chance.’ “

Maybe not. But a career Grand Slam hardly seems like a stretch anymore.

“I think that that’s the sign of the complete great player. And I’m a leg away. And it’s been a tough leg for me,” Mickelson said to laughter, “but I think that’s the sign. I think there’s five players that have done that. And those five players are the greats of the game. You look at them with a different light.

“And if I were able to ever win a U.S. Open, and I’m very hopeful that I will — but it has been elusive for me. And yet,” he said finally, “this championship has been much harder for me to get.”

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Jim Litke is a national sports columnist for The Associated Press. Write to him at jlitke@ap.org and follow him at Twitter.com/Jim Litke.